6533b7d9fe1ef96bd126ba2c

RESEARCH PRODUCT

Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac

Christiane MartinAlain Piard

subject

Discrete mathematicsPure mathematics17B10Statistical and Nonlinear PhysicsUniversal enveloping algebraLie superalgebraAffine Lie algebra17B68Lie conformal algebraGraded Lie algebraAlgebra representationVirasoro algebraMathematics::Representation TheoryIndecomposable moduleMathematical PhysicsMathematics

description

We consider a class of indecomposable modules over the Virasoro Lie algebra that we call bounded admissible modules. We get results concerning the center and the dimensions of the weight spaces. We prove that these modules always contain a submodule with one-dimensional weight spaces. From this follows the proof of a conjecture of V. Kac concerning the classification of simple admissible modules.

yearjournalcountryeditionlanguage
1991-03-01Communications in Mathematical Physics
https://doi.org/10.1007/bf02099118